Question

Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110 reservations. Define the random variable \(x\) as \(x=\) the number of people who actually show up for a sold-out flight on this plane

Short answer

The random variable \(x\) in this exercise is a numerical representation of the outcome of a random phenomenon, namely the number of passengers showing up for a flight. The variable can take any value ranging from 0 to 110.

Step-by-step solution

Define the Random Variable

The random variable in this exercise is defined as \(x =\) the number of people who actually show up for a sold-out flight on a plane. This variable is called a random variable because its exact value is not known until the event (in this case, the actual flight) takes place. In statistical terms, a random variable is a variable whose possible values are numerical outcomes of a random phenomenon.

Identify the Range for the Random Variable

In this situation, the number of people who could potentially show up for the flight ranges from 0 to 110. This is because 110 reservations were made, but it's also possible that no one shows up. Therefore, the random variable \(x\) can take any value from 0 through 110.

Understand the Application of the Random Variable

In this context, the random variable \(x\) helps us analyze the situation and make predictions about the flight. For example, the airline can use the probability distribution of \(x\) to predict the likely number of passengers, plan for possible overbooking scenarios, adjust their reservations strategy, etc.